On the mean value of the square of a generalized Dedekind sum (Q1601117)
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scientific article; zbMATH DE number 1757278
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the mean value of the square of a generalized Dedekind sum |
scientific article; zbMATH DE number 1757278 |
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On the mean value of the square of a generalized Dedekind sum (English)
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19 June 2002
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The authors deduce a mean value formula for the square of the modulus of generalized Dedekind sums \[ S(h,n,q)= \sum_{a=1}^q \overline{B}_n \biggl( \frac{a}{q} \biggr) \overline{B}_n \biggl( \frac{ah}{q} \biggr), \] where \(\overline{B}_n(\cdot)\) is the \(n\)th Bernoulli periodic function. The proof makes use of a representation in terms of Dirichlet \(L\)-functions obtained by \textit{W. P. Zhang} [Acta Math. Sin. 44, 269-272 (2001)].
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mean value formula
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generalized Dedekind sums
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